For the most part, I found the usability of Google+ to be much better than most social networking apps. With icons spread far apart on the home screen, it's easy to tap directly on one of them while on the move.
The Stream, which is the main flow of commentary from the world, is divided into three tributaries -- Incoming, Circles, and Nearby. Incoming consists of comments from just about anyone who is on Google+, Circles consists of talk from those people you have added to your circles, and Nearby is a new feature that shows posts by people who are in the same geographical area as you. To switch between these three flows of information, you do a sideways swipe on the screen. It's very natural and well thought out.
The Google+ app gives you most of the functionality of the website without any of the fluff. One thing that immediately bothered me about the web version of the service is that when some Internet celebrity (I'm looking at you, Chris Pirillo) posts something, there are immediately hundreds of comments. The web version lists all of those comments by default; you can hide them with a click of an icon, but I'd rather that it be the other way around.
With the app, the opposite happens -- I can see that 150 people gave a +1 to a Sergey Brin post about recumbent road bikes and that there 191 comments. If I actually feel like reading those, I can, but if I'm inclined to ignore them I can just keep scrolling through the stream of posts.
One other nice feature of the Google+ app is the Foursquare-killing ability to check into a location. There's a little "checkbox" icon that brings up the checkin screen. It lists a number of nearby businesses, so you're immediately able to check in with a tap.
Posting photos to Google+ is now easier than ever, as it's accomplished within the app. Any post can have a photo attached from either your iPhone camera or Photo Library, and you can choose whether or not you wish to have the image geolocated.
I like the ability to use Google+ emphasis shortcuts -- *bold* and _italics_ in my Google+ posts. It's a nice way to add emphasis quickly, and the the readability of the emphatic text is nice. That being said, I'd like to see a way to change the default text size in the app. It's a little on the small side, and although I can read it just fine I know there are many people who might find it unreadable.
The ability to create a Huddle (group chat) with friends on Google+ is something that is specific to the app. It's not on the website. There's probably a reason for that, since on the website you can do a full video Hangout with your buddies. Still, it would be nice for the app and the website to be consistent -- either add the Hangout feature to the Google+ app or the Huddle feature to the website.
For a first go at an app for a completely new social networking service, the Google+ iPhone app is remarkably well designed and executed. Since I'm not running an iOS 5 beta on my iPhone, the app is stable, and I can see how Google+ could easily become my social network of choice. That's incredibly hard for me to say, because I'm not really a fan of Google. So far the Google+ service seems "just right" compared to the unending flood of tweets and Facebook updates I get. That may change when the rest of the world gets onto Google+, but by keeping my circles small, at least I can control the torrent. The Google+ app adds another layer of icing to the Google+ cake.